LMFDB - Embedded newform 74.5.d.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,5,Mod(31,74)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	74.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.64937726820$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 727 x^{12} + 207381 x^{10} + 29788577 x^{8} + 2302194203 x^{6} + 92916575085 x^{4} + \cdots + 6531254919424 $ x^14 + 727x^12 + 207381x^10 + 29788577x^8 + 2302194203x^6 + 92916575085x^4 + 1658451585508x^2 + 6531254919424
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.2
Root			$-9.07204i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.5.d.b.43.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} -10.0720i q^{3} +8.00000i q^{4} +(-28.1665 + 28.1665i) q^{5} +(20.1441 - 20.1441i) q^{6} -38.8317 q^{7} +(-16.0000 + 16.0000i) q^{8} -20.4460 q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} -10.0720i q^{3} +8.00000i q^{4} +(-28.1665 + 28.1665i) q^{5} +(20.1441 - 20.1441i) q^{6} -38.8317 q^{7} +(-16.0000 + 16.0000i) q^{8} -20.4460 q^{9} -112.666 q^{10} +22.9963i q^{11} +80.5763 q^{12} +(-217.186 + 217.186i) q^{13} +(-77.6634 - 77.6634i) q^{14} +(283.694 + 283.694i) q^{15} -64.0000 q^{16} +(14.6589 - 14.6589i) q^{17} +(-40.8920 - 40.8920i) q^{18} +(-1.78171 + 1.78171i) q^{19} +(-225.332 - 225.332i) q^{20} +391.114i q^{21} +(-45.9926 + 45.9926i) q^{22} +(-1.16603 + 1.16603i) q^{23} +(161.153 + 161.153i) q^{24} -961.706i q^{25} -868.745 q^{26} -609.902i q^{27} -310.653i q^{28} +(-1136.92 - 1136.92i) q^{29} +1134.78i q^{30} +(875.501 + 875.501i) q^{31} +(-128.000 - 128.000i) q^{32} +231.620 q^{33} +58.6355 q^{34} +(1093.75 - 1093.75i) q^{35} -163.568i q^{36} +(1150.10 + 742.579i) q^{37} -7.12685 q^{38} +(2187.51 + 2187.51i) q^{39} -901.329i q^{40} +2318.93i q^{41} +(-782.229 + 782.229i) q^{42} +(1238.87 - 1238.87i) q^{43} -183.970 q^{44} +(575.892 - 575.892i) q^{45} -4.66411 q^{46} -262.585 q^{47} +644.611i q^{48} -893.100 q^{49} +(1923.41 - 1923.41i) q^{50} +(-147.645 - 147.645i) q^{51} +(-1737.49 - 1737.49i) q^{52} -478.300 q^{53} +(1219.80 - 1219.80i) q^{54} +(-647.725 - 647.725i) q^{55} +(621.307 - 621.307i) q^{56} +(17.9455 + 17.9455i) q^{57} -4547.67i q^{58} +(-1172.91 + 1172.91i) q^{59} +(-2269.55 + 2269.55i) q^{60} +(947.553 + 947.553i) q^{61} +3502.01i q^{62} +793.952 q^{63} -512.000i q^{64} -12234.8i q^{65} +(463.239 + 463.239i) q^{66} +5751.96i q^{67} +(117.271 + 117.271i) q^{68} +(11.7443 + 11.7443i) q^{69} +4375.01 q^{70} +3097.13 q^{71} +(327.136 - 327.136i) q^{72} -2486.65i q^{73} +(815.050 + 3785.36i) q^{74} -9686.34 q^{75} +(-14.2537 - 14.2537i) q^{76} -892.985i q^{77} +8750.03i q^{78} +(-5827.19 + 5827.19i) q^{79} +(1802.66 - 1802.66i) q^{80} -7799.09 q^{81} +(-4637.87 + 4637.87i) q^{82} -10094.2 q^{83} -3128.91 q^{84} +825.779i q^{85} +4955.49 q^{86} +(-11451.1 + 11451.1i) q^{87} +(-367.941 - 367.941i) q^{88} +(9315.73 + 9315.73i) q^{89} +2303.57 q^{90} +(8433.71 - 8433.71i) q^{91} +(-9.32822 - 9.32822i) q^{92} +(8818.09 - 8818.09i) q^{93} +(-525.169 - 525.169i) q^{94} -100.369i q^{95} +(-1289.22 + 1289.22i) q^{96} +(1566.19 - 1566.19i) q^{97} +(-1786.20 - 1786.20i) q^{98} -470.182i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9}+O(q^{10}) $ 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9} + 144 q^{10} + 160 q^{12} - 104 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} + 516 q^{17} - 692 q^{18} - 328 q^{19} + 288 q^{20} - 320 q^{22} + 154 q^{23} + 320 q^{24} - 416 q^{26} + 1686 q^{29} + 3834 q^{31} - 1792 q^{32} + 2104 q^{33} + 2064 q^{34} - 1502 q^{35} + 2640 q^{37} - 1312 q^{38} - 4526 q^{39} - 5984 q^{42} + 3616 q^{43} - 1280 q^{44} - 2238 q^{45} + 616 q^{46} - 6892 q^{47} + 12854 q^{49} + 7516 q^{50} - 6742 q^{51} - 832 q^{52} + 12572 q^{53} - 1072 q^{54} + 5510 q^{55} + 768 q^{56} - 6302 q^{57} - 8422 q^{59} + 3024 q^{60} - 6386 q^{61} + 22244 q^{63} + 4208 q^{66} + 4128 q^{68} + 1728 q^{69} - 6008 q^{70} + 8680 q^{71} + 5536 q^{72} + 1316 q^{74} - 37980 q^{75} - 2624 q^{76} - 28520 q^{79} - 2304 q^{80} - 33962 q^{81} + 9136 q^{82} - 22688 q^{83} - 23936 q^{84} + 14464 q^{86} + 1828 q^{87} - 2560 q^{88} + 18344 q^{89} - 8952 q^{90} - 4918 q^{91} + 1232 q^{92} + 24 q^{93} - 13784 q^{94} - 2560 q^{96} + 23246 q^{97} + 25708 q^{98}+O(q^{100}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9 + 144 * q^10 + 160 * q^12 - 104 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 + 516 * q^17 - 692 * q^18 - 328 * q^19 + 288 * q^20 - 320 * q^22 + 154 * q^23 + 320 * q^24 - 416 * q^26 + 1686 * q^29 + 3834 * q^31 - 1792 * q^32 + 2104 * q^33 + 2064 * q^34 - 1502 * q^35 + 2640 * q^37 - 1312 * q^38 - 4526 * q^39 - 5984 * q^42 + 3616 * q^43 - 1280 * q^44 - 2238 * q^45 + 616 * q^46 - 6892 * q^47 + 12854 * q^49 + 7516 * q^50 - 6742 * q^51 - 832 * q^52 + 12572 * q^53 - 1072 * q^54 + 5510 * q^55 + 768 * q^56 - 6302 * q^57 - 8422 * q^59 + 3024 * q^60 - 6386 * q^61 + 22244 * q^63 + 4208 * q^66 + 4128 * q^68 + 1728 * q^69 - 6008 * q^70 + 8680 * q^71 + 5536 * q^72 + 1316 * q^74 - 37980 * q^75 - 2624 * q^76 - 28520 * q^79 - 2304 * q^80 - 33962 * q^81 + 9136 * q^82 - 22688 * q^83 - 23936 * q^84 + 14464 * q^86 + 1828 * q^87 - 2560 * q^88 + 18344 * q^89 - 8952 * q^90 - 4918 * q^91 + 1232 * q^92 + 24 * q^93 - 13784 * q^94 - 2560 * q^96 + 23246 * q^97 + 25708 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$		−	10.0720i		−	1.11912i	−0.828791	−	0.559558i	$-0.810971\pi$
$3$		−	10.0720i		−	1.11912i	0.828791	−	0.559558i	$-0.189029\pi$
$4$			8.00000i			0.500000i
$5$	−28.1665	+	28.1665i	−1.12666	+	1.12666i	−0.135944	+	0.990716i	$0.543407\pi$
$5$	−28.1665	+	28.1665i	−1.12666	+	1.12666i	−0.990716	+	0.135944i	$0.956593\pi$
$6$	20.1441	−	20.1441i	0.559558	−	0.559558i
$7$	−38.8317			−0.792483			−0.396242	−	0.918146i	$-0.629686\pi$
$7$	−38.8317			−0.792483			−0.396242	+	0.918146i	$0.629686\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	−20.4460			−0.252420
$10$	−112.666			−1.12666
$11$			22.9963i			0.190052i	0.995475	+	0.0950260i	$0.0302934\pi$
$11$			22.9963i			0.190052i	−0.995475	+	0.0950260i	$0.969707\pi$
$12$	80.5763			0.559558
$13$	−217.186	+	217.186i	−1.28513	+	1.28513i	−0.347414	+	0.937712i	$0.612940\pi$
$13$	−217.186	+	217.186i	−1.28513	+	1.28513i	−0.937712	+	0.347414i	$0.887060\pi$
$14$	−77.6634	−	77.6634i	−0.396242	−	0.396242i
$15$	283.694	+	283.694i	1.26086	+	1.26086i
$16$	−64.0000			−0.250000
$17$	14.6589	−	14.6589i	0.0507228	−	0.0507228i	−0.681290	−	0.732013i	$-0.738581\pi$
$17$	14.6589	−	14.6589i	0.0507228	−	0.0507228i	0.732013	+	0.681290i	$0.238581\pi$
$18$	−40.8920	−	40.8920i	−0.126210	−	0.126210i
$19$	−1.78171	+	1.78171i	−0.00493549	+	0.00493549i	−0.709570	−	0.704635i	$-0.751111\pi$
$19$	−1.78171	+	1.78171i	−0.00493549	+	0.00493549i	0.704635	+	0.709570i	$0.251111\pi$
$20$	−225.332	−	225.332i	−0.563330	−	0.563330i
$21$			391.114i			0.886880i
$22$	−45.9926	+	45.9926i	−0.0950260	+	0.0950260i
$23$	−1.16603	+	1.16603i	−0.00220421	+	0.00220421i	−0.708208	−	0.706004i	$-0.750496\pi$
$23$	−1.16603	+	1.16603i	−0.00220421	+	0.00220421i	0.706004	+	0.708208i	$0.250496\pi$
$24$	161.153	+	161.153i	0.279779	+	0.279779i
$25$		−	961.706i		−	1.53873i
$26$	−868.745			−1.28513
$27$		−	609.902i		−	0.836629i
$28$		−	310.653i		−	0.396242i
$29$	−1136.92	−	1136.92i	−1.35186	−	1.35186i	−0.883575	−	0.468289i	$-0.844870\pi$
$29$	−1136.92	−	1136.92i	−1.35186	−	1.35186i	−0.468289	−	0.883575i	$-0.655130\pi$
$30$			1134.78i			1.26086i
$31$	875.501	+	875.501i	0.911032	+	0.911032i	0.996353	−	0.0853217i	$-0.0271918\pi$
$31$	875.501	+	875.501i	0.911032	+	0.911032i	−0.0853217	+	0.996353i	$0.527192\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	231.620			0.212690
$34$	58.6355			0.0507228
$35$	1093.75	−	1093.75i	0.892860	−	0.892860i
$36$		−	163.568i		−	0.126210i
$37$	1150.10	+	742.579i	0.840105	+	0.542424i
$37$	1150.10	+	742.579i	0.840105	+	0.542424i
$38$	−7.12685			−0.00493549
$39$	2187.51	+	2187.51i	1.43820	+	1.43820i
$40$		−	901.329i		−	0.563330i
$41$			2318.93i			1.37950i	0.724049	+	0.689748i	$0.242279\pi$
$41$			2318.93i			1.37950i	−0.724049	+	0.689748i	$0.757721\pi$
$42$	−782.229	+	782.229i	−0.443440	+	0.443440i
$43$	1238.87	−	1238.87i	0.670023	−	0.670023i	−0.287698	−	0.957721i	$-0.592890\pi$
$43$	1238.87	−	1238.87i	0.670023	−	0.670023i	0.957721	+	0.287698i	$0.0928900\pi$
$44$	−183.970			−0.0950260
$45$	575.892	−	575.892i	0.284391	−	0.284391i
$46$	−4.66411			−0.00220421
$47$	−262.585			−0.118870			−0.0594352	−	0.998232i	$-0.518930\pi$
$47$	−262.585			−0.118870			−0.0594352	+	0.998232i	$0.518930\pi$
$48$			644.611i			0.279779i
$49$	−893.100			−0.371970
$50$	1923.41	−	1923.41i	0.769365	−	0.769365i
$51$	−147.645	−	147.645i	−0.0567646	−	0.0567646i
$52$	−1737.49	−	1737.49i	−0.642563	−	0.642563i
$53$	−478.300			−0.170274			−0.0851371	−	0.996369i	$-0.527133\pi$
$53$	−478.300			−0.170274			−0.0851371	+	0.996369i	$0.527133\pi$
$54$	1219.80	−	1219.80i	0.418314	−	0.418314i
$55$	−647.725	−	647.725i	−0.214124	−	0.214124i
$56$	621.307	−	621.307i	0.198121	−	0.198121i
$57$	17.9455	+	17.9455i	0.00552338	+	0.00552338i
$58$		−	4547.67i		−	1.35186i
$59$	−1172.91	+	1172.91i	−0.336947	+	0.336947i	−0.855217	−	0.518270i	$-0.826576\pi$
$59$	−1172.91	+	1172.91i	−0.336947	+	0.336947i	0.518270	+	0.855217i	$0.326576\pi$
$60$	−2269.55	+	2269.55i	−0.630432	+	0.630432i
$61$	947.553	+	947.553i	0.254650	+	0.254650i	0.822874	−	0.568224i	$-0.192369\pi$
$61$	947.553	+	947.553i	0.254650	+	0.254650i	−0.568224	+	0.822874i	$0.692369\pi$
$62$			3502.01i			0.911032i
$63$	793.952			0.200038
$64$		−	512.000i		−	0.125000i
$65$		−	12234.8i		−	2.89580i
$66$	463.239	+	463.239i	0.106345	+	0.106345i
$67$			5751.96i			1.28135i	0.767814	+	0.640673i	$0.221344\pi$
$67$			5751.96i			1.28135i	−0.767814	+	0.640673i	$0.778656\pi$
$68$	117.271	+	117.271i	0.0253614	+	0.0253614i
$69$	11.7443	+	11.7443i	0.00246677	+	0.00246677i
$70$	4375.01			0.892860
$71$	3097.13			0.614389			0.307194	−	0.951647i	$-0.400610\pi$
$71$	3097.13			0.614389			0.307194	+	0.951647i	$0.400610\pi$
$72$	327.136	−	327.136i	0.0631049	−	0.0631049i
$73$		−	2486.65i		−	0.466627i	−0.972402	−	0.233313i	$-0.925043\pi$
$73$		−	2486.65i		−	0.466627i	0.972402	−	0.233313i	$-0.0749568\pi$
$74$	815.050	+	3785.36i	0.148840	+	0.691264i
$75$	−9686.34			−1.72202
$76$	−14.2537	−	14.2537i	−0.00246774	−	0.00246774i
$77$		−	892.985i		−	0.150613i
$78$			8750.03i			1.43820i
$79$	−5827.19	+	5827.19i	−0.933695	+	0.933695i	−0.997935	−	0.0642395i	$-0.979538\pi$
$79$	−5827.19	+	5827.19i	−0.933695	+	0.933695i	0.0642395	+	0.997935i	$0.479538\pi$
$80$	1802.66	−	1802.66i	0.281665	−	0.281665i
$81$	−7799.09			−1.18870
$82$	−4637.87	+	4637.87i	−0.689748	+	0.689748i
$83$	−10094.2			−1.46526			−0.732631	−	0.680626i	$-0.761708\pi$
$83$	−10094.2			−1.46526			−0.732631	+	0.680626i	$0.761708\pi$
$84$	−3128.91			−0.443440
$85$			825.779i			0.114295i
$86$	4955.49			0.670023
$87$	−11451.1	+	11451.1i	−1.51289	+	1.51289i
$88$	−367.941	−	367.941i	−0.0475130	−	0.0475130i
$89$	9315.73	+	9315.73i	1.17608	+	1.17608i	0.980735	+	0.195345i	$0.0625826\pi$
$89$	9315.73	+	9315.73i	1.17608	+	1.17608i	0.195345	+	0.980735i	$0.437417\pi$
$90$	2303.57			0.284391
$91$	8433.71	−	8433.71i	1.01844	−	1.01844i
$92$	−9.32822	−	9.32822i	−0.00110211	−	0.00110211i
$93$	8818.09	−	8818.09i	1.01955	−	1.01955i
$94$	−525.169	−	525.169i	−0.0594352	−	0.0594352i
$95$		−	100.369i		−	0.0111212i
$96$	−1289.22	+	1289.22i	−0.139889	+	0.139889i
$97$	1566.19	−	1566.19i	0.166457	−	0.166457i	−0.618963	−	0.785420i	$-0.712447\pi$
$97$	1566.19	−	1566.19i	0.166457	−	0.166457i	0.785420	+	0.618963i	$0.212447\pi$
$98$	−1786.20	−	1786.20i	−0.185985	−	0.185985i
$99$		−	470.182i		−	0.0479728i
$100$	7693.65			0.769365
$101$			6946.09i			0.680923i	0.940259	+	0.340461i	$0.110583\pi$
$101$			6946.09i			0.680923i	−0.940259	+	0.340461i	$0.889417\pi$
$102$		−	590.579i		−	0.0567646i
$103$	9808.29	+	9808.29i	0.924525	+	0.924525i	0.997345	−	0.0728201i	$-0.0231999\pi$
$103$	9808.29	+	9808.29i	0.924525	+	0.924525i	−0.0728201	+	0.997345i	$0.523200\pi$
$104$		−	6949.96i		−	0.642563i
$105$	−11016.3	−	11016.3i	−0.999213	−	0.999213i
$106$	−956.601	−	956.601i	−0.0851371	−	0.0851371i
$107$	−22204.2			−1.93940			−0.969702	−	0.244291i	$-0.921445\pi$
$107$	−22204.2			−1.93940			−0.969702	+	0.244291i	$0.921445\pi$
$108$	4879.22			0.418314
$109$	530.211	−	530.211i	0.0446268	−	0.0446268i	−0.684441	−	0.729068i	$-0.739954\pi$
$109$	530.211	−	530.211i	0.0446268	−	0.0446268i	0.729068	+	0.684441i	$0.239954\pi$
$110$		−	2590.90i		−	0.214124i
$111$	7479.28	−	11583.9i	0.607035	−	0.940174i
$112$	2485.23			0.198121
$113$	−10292.3	−	10292.3i	−0.806038	−	0.806038i	0.177994	−	0.984032i	$-0.443039\pi$
$113$	−10292.3	−	10292.3i	−0.806038	−	0.806038i	−0.984032	+	0.177994i	$0.943039\pi$
$114$			71.7819i			0.00552338i
$115$		−	65.6859i		−	0.00496680i
$116$	9095.34	−	9095.34i	0.675932	−	0.675932i
$117$	4440.59	−	4440.59i	0.324391	−	0.324391i
$118$	−4691.64			−0.336947
$119$	−569.229	+	569.229i	−0.0401970	+	0.0401970i
$120$	−9078.22			−0.630432
$121$	14112.2			0.963880
$122$			3790.21i			0.254650i
$123$	23356.4			1.54382
$124$	−7004.01	+	7004.01i	−0.455516	+	0.455516i
$125$	9483.84	+	9483.84i	0.606965	+	0.606965i
$126$	1587.90	+	1587.90i	0.100019	+	0.100019i
$127$	−9319.34			−0.577800			−0.288900	−	0.957359i	$-0.593290\pi$
$127$	−9319.34			−0.577800			−0.288900	+	0.957359i	$0.593290\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$	−12478.0	−	12478.0i	−0.749833	−	0.749833i
$130$	24469.5	−	24469.5i	1.44790	−	1.44790i
$131$	14192.4	+	14192.4i	0.827014	+	0.827014i	0.987103	−	0.160088i	$-0.0511779\pi$
$131$	14192.4	+	14192.4i	0.827014	+	0.827014i	−0.160088	+	0.987103i	$0.551178\pi$
$132$			1852.96i			0.106345i
$133$	69.1869	−	69.1869i	0.00391129	−	0.00391129i
$134$	−11503.9	+	11503.9i	−0.640673	+	0.640673i
$135$	17178.8	+	17178.8i	0.942597	+	0.942597i
$136$			469.084i			0.0253614i
$137$	4856.56			0.258754			0.129377	−	0.991595i	$-0.458702\pi$
$137$	4856.56			0.258754			0.129377	+	0.991595i	$0.458702\pi$
$138$			46.9771i			0.00246677i
$139$		−	32105.8i		−	1.66170i	−0.556493	−	0.830852i	$-0.687853\pi$
$139$		−	32105.8i		−	1.66170i	0.556493	−	0.830852i	$-0.312147\pi$
$140$	8750.03	+	8750.03i	0.446430	+	0.446430i
$141$			2644.76i			0.133030i
$142$	6194.27	+	6194.27i	0.307194	+	0.307194i
$143$	−4994.48	−	4994.48i	−0.244241	−	0.244241i
$144$	1308.54			0.0631049
$145$	64046.1			3.04619
$146$	4973.31	−	4973.31i	0.233313	−	0.233313i
$147$			8995.34i			0.416278i
$148$	−5940.63	+	9200.83i	−0.271212	+	0.420052i
$149$	−24562.0			−1.10634			−0.553172	−	0.833067i	$-0.686583\pi$
$149$	−24562.0			−1.10634			−0.553172	+	0.833067i	$0.686583\pi$
$150$	−19372.7	−	19372.7i	−0.861008	−	0.861008i
$151$			23750.3i			1.04163i	0.853668	+	0.520817i	$0.174373\pi$
$151$			23750.3i			1.04163i	−0.853668	+	0.520817i	$0.825627\pi$
$152$		−	57.0148i		−	0.00246774i
$153$	−299.715	+	299.715i	−0.0128034	+	0.0128034i
$154$	1785.97	−	1785.97i	0.0753065	−	0.0753065i
$155$	−49319.7			−2.05285
$156$	−17500.1	+	17500.1i	−0.719102	+	0.719102i
$157$	−7486.27			−0.303715			−0.151857	−	0.988402i	$-0.548525\pi$
$157$	−7486.27			−0.303715			−0.151857	+	0.988402i	$0.548525\pi$
$158$	−23308.8			−0.933695
$159$			4817.46i			0.190557i
$160$	7210.63			0.281665
$161$	45.2788	−	45.2788i	0.00174680	−	0.00174680i
$162$	−15598.2	−	15598.2i	−0.594352	−	0.594352i
$163$	450.447	+	450.447i	0.0169539	+	0.0169539i	0.715533	−	0.698579i	$-0.246184\pi$
$163$	450.447	+	450.447i	0.0169539	+	0.0169539i	−0.698579	+	0.715533i	$0.746184\pi$
$164$	−18551.5			−0.689748
$165$	−6523.92	+	6523.92i	−0.239630	+	0.239630i
$166$	−20188.4	−	20188.4i	−0.732631	−	0.732631i
$167$	4669.75	−	4669.75i	0.167440	−	0.167440i	−0.618413	−	0.785853i	$-0.712224\pi$
$167$	4669.75	−	4669.75i	0.167440	−	0.167440i	0.785853	+	0.618413i	$0.212224\pi$
$168$	−6257.83	−	6257.83i	−0.221720	−	0.221720i
$169$		−	65778.7i		−	2.30310i
$170$	−1651.56	+	1651.56i	−0.0571474	+	0.0571474i
$171$	36.4289	−	36.4289i	0.00124581	−	0.00124581i
$172$	9910.98	+	9910.98i	0.335011	+	0.335011i
$173$			39422.8i			1.31721i	0.752488	+	0.658605i	$0.228853\pi$
$173$			39422.8i			1.31721i	−0.752488	+	0.658605i	$0.771147\pi$
$174$	−45804.3			−1.51289
$175$			37344.7i			1.21942i
$176$		−	1471.76i		−	0.0475130i
$177$	11813.6	+	11813.6i	0.377082	+	0.377082i
$178$			37262.9i			1.17608i
$179$	18007.4	+	18007.4i	0.562012	+	0.562012i	0.929879	−	0.367866i	$-0.119912\pi$
$179$	18007.4	+	18007.4i	0.562012	+	0.562012i	−0.367866	+	0.929879i	$0.619912\pi$
$180$	4607.14	+	4607.14i	0.142196	+	0.142196i
$181$	28738.9			0.877229			0.438614	−	0.898675i	$-0.355469\pi$
$181$	28738.9			0.877229			0.438614	+	0.898675i	$0.355469\pi$
$182$	33734.8			1.01844
$183$	9543.79	−	9543.79i	0.284983	−	0.284983i
$184$		−	37.3129i		−	0.00110211i
$185$	−53310.3	+	11478.6i	−1.55764	+	0.335385i
$186$	35272.3			1.01955
$187$	337.100	+	337.100i	0.00963996	+	0.00963996i
$188$		−	2100.68i		−	0.0594352i
$189$			23683.5i			0.663014i
$190$	200.739	−	200.739i	0.00556062	−	0.00556062i
$191$	37791.0	−	37791.0i	1.03591	−	1.03591i	0.0365788	−	0.999331i	$-0.488354\pi$
$191$	37791.0	−	37791.0i	1.03591	−	1.03591i	0.999331	−	0.0365788i	$-0.0116460\pi$
$192$	−5156.88			−0.139889
$193$	40742.3	−	40742.3i	1.09378	−	1.09378i	0.0986626	−	0.995121i	$-0.468544\pi$
$193$	40742.3	−	40742.3i	1.09378	−	1.09378i	0.995121	−	0.0986626i	$-0.0314565\pi$
$194$	6264.77			0.166457
$195$	−123229.			−3.24074
$196$		−	7144.80i		−	0.185985i
$197$	−69226.9			−1.78378			−0.891892	−	0.452247i	$-0.850622\pi$
$197$	−69226.9			−1.78378			−0.891892	+	0.452247i	$0.850622\pi$
$198$	940.363	−	940.363i	0.0239864	−	0.0239864i
$199$	34784.5	+	34784.5i	0.878375	+	0.878375i	0.993367	−	0.114991i	$-0.0366839\pi$
$199$	34784.5	+	34784.5i	0.878375	+	0.878375i	−0.114991	+	0.993367i	$0.536684\pi$
$200$	15387.3	+	15387.3i	0.384682	+	0.384682i
$201$	57934.0			1.43397
$202$	−13892.2	+	13892.2i	−0.340461	+	0.340461i
$203$	44148.4	+	44148.4i	1.07133	+	1.07133i
$204$	1181.16	−	1181.16i	0.0283823	−	0.0283823i
$205$	−65316.3	−	65316.3i	−1.55423	−	1.55423i
$206$			39233.1i			0.924525i
$207$	23.8406	−	23.8406i	0.000556386	−	0.000556386i
$208$	13899.9	−	13899.9i	0.321281	−	0.321281i
$209$	−40.9728	−	40.9728i	−0.000938000	−	0.000938000i
$210$		−	44065.3i		−	0.999213i
$211$	15182.4			0.341017			0.170508	−	0.985356i	$-0.445459\pi$
$211$	15182.4			0.341017			0.170508	+	0.985356i	$0.445459\pi$
$212$		−	3826.40i		−	0.0851371i
$213$		−	31194.5i		−	0.687572i
$214$	−44408.5	−	44408.5i	−0.969702	−	0.969702i
$215$			69789.4i			1.50978i
$216$	9758.44	+	9758.44i	0.209157	+	0.209157i
$217$	−33997.2	−	33997.2i	−0.721977	−	0.721977i
$218$	2120.84			0.0446268
$219$	−25045.7			−0.522209
$220$	5181.80	−	5181.80i	0.107062	−	0.107062i
$221$			6367.41i			0.130370i
$222$	38126.3	−	8209.21i	0.773605	−	0.166570i
$223$	−44851.7			−0.901921			−0.450961	−	0.892544i	$-0.648919\pi$
$223$	−44851.7			−0.901921			−0.450961	+	0.892544i	$0.648919\pi$
$224$	4970.46	+	4970.46i	0.0990604	+	0.0990604i
$225$			19663.0i			0.388405i
$226$		−	41169.2i		−	0.806038i
$227$	26998.5	−	26998.5i	0.523947	−	0.523947i	−0.394814	−	0.918761i	$-0.629191\pi$
$227$	26998.5	−	26998.5i	0.523947	−	0.523947i	0.918761	+	0.394814i	$0.129191\pi$
$228$	−143.564	+	143.564i	−0.00276169	+	0.00276169i
$229$	44311.5			0.844979			0.422489	−	0.906368i	$-0.361156\pi$
$229$	44311.5			0.844979			0.422489	+	0.906368i	$0.361156\pi$
$230$	131.372	−	131.372i	0.00248340	−	0.00248340i
$231$	−8994.18			−0.168553
$232$	36381.4			0.675932
$233$		−	71698.4i		−	1.32068i	−0.750966	−	0.660340i	$-0.770412\pi$
$233$		−	71698.4i		−	1.32068i	0.750966	−	0.660340i	$-0.229588\pi$
$234$	17762.3			0.324391
$235$	7396.10	−	7396.10i	0.133927	−	0.133927i
$236$	−9383.29	−	9383.29i	−0.168473	−	0.168473i
$237$	58691.7	+	58691.7i	1.04491	+	1.04491i
$238$	−2276.92			−0.0401970
$239$	34157.5	−	34157.5i	0.597985	−	0.597985i	−0.341791	−	0.939776i	$-0.611033\pi$
$239$	34157.5	−	34157.5i	0.597985	−	0.597985i	0.939776	+	0.341791i	$0.111033\pi$
$240$	−18156.4	−	18156.4i	−0.315216	−	0.315216i
$241$	8222.20	−	8222.20i	0.141564	−	0.141564i	−0.632773	−	0.774337i	$-0.718083\pi$
$241$	8222.20	−	8222.20i	0.141564	−	0.141564i	0.774337	+	0.632773i	$0.218083\pi$
$242$	28224.3	+	28224.3i	0.481940	+	0.481940i
$243$			29150.6i			0.493668i
$244$	−7580.42	+	7580.42i	−0.127325	+	0.127325i
$245$	25155.5	−	25155.5i	0.419084	−	0.419084i
$246$	46712.8	+	46712.8i	0.771908	+	0.771908i
$247$		−	773.927i		−	0.0126854i
$248$	−28016.0			−0.455516
$249$			101669.i			1.63980i
$250$			37935.3i			0.606965i
$251$	3118.14	+	3118.14i	0.0494935	+	0.0494935i	0.731420	−	0.681927i	$-0.238858\pi$
$251$	3118.14	+	3118.14i	0.0494935	+	0.0494935i	−0.681927	+	0.731420i	$0.738858\pi$
$252$			6351.62i			0.100019i
$253$	−26.8143	−	26.8143i	−0.000418915	−	0.000418915i
$254$	−18638.7	−	18638.7i	−0.288900	−	0.288900i
$255$	8317.28			0.127909
$256$	4096.00			0.0625000
$257$	−40782.9	+	40782.9i	−0.617465	+	0.617465i	−0.944880	−	0.327416i	$-0.893822\pi$
$257$	−40782.9	+	40782.9i	−0.617465	+	0.617465i	0.327416	+	0.944880i	$0.393822\pi$
$258$		−	49911.9i		−	0.749833i
$259$	−44660.5	−	28835.6i	−0.665769	−	0.429862i
$260$	97878.1			1.44790
$261$	23245.4	+	23245.4i	0.341237	+	0.341237i
$262$			56769.6i			0.827014i
$263$		−	132264.i		−	1.91219i	−0.293061	−	0.956094i	$-0.594674\pi$
$263$		−	132264.i		−	1.91219i	0.293061	−	0.956094i	$-0.405326\pi$
$264$	−3705.91	+	3705.91i	−0.0531725	+	0.0531725i
$265$	13472.1	−	13472.1i	0.191841	−	0.191841i
$266$	276.747			0.00391129
$267$	93828.4	−	93828.4i	1.31617	−	1.31617i
$268$	−46015.7			−0.640673
$269$	−113409.			−1.56726			−0.783632	−	0.621226i	$-0.786635\pi$
$269$	−113409.			−1.56726			−0.783632	+	0.621226i	$0.786635\pi$
$270$			68715.3i			0.942597i
$271$	−47200.0			−0.642693			−0.321346	−	0.946962i	$-0.604135\pi$
$271$	−47200.0			−0.642693			−0.321346	+	0.946962i	$0.604135\pi$
$272$	−938.168	+	938.168i	−0.0126807	+	0.0126807i
$273$	−84944.6	−	84944.6i	−1.13975	−	1.13975i
$274$	9713.11	+	9713.11i	0.129377	+	0.129377i
$275$	22115.7			0.292439
$276$	−93.9542	+	93.9542i	−0.00123338	+	0.00123338i
$277$	42300.9	+	42300.9i	0.551303	+	0.551303i	0.926817	−	0.375514i	$-0.122534\pi$
$277$	42300.9	+	42300.9i	0.551303	+	0.551303i	−0.375514	+	0.926817i	$0.622534\pi$
$278$	64211.6	−	64211.6i	0.830852	−	0.830852i
$279$	−17900.5	−	17900.5i	−0.229962	−	0.229962i
$280$			35000.1i			0.446430i
$281$	−34291.2	+	34291.2i	−0.434280	+	0.434280i	−0.890082	−	0.455801i	$-0.849353\pi$
$281$	−34291.2	+	34291.2i	−0.434280	+	0.434280i	0.455801	+	0.890082i	$0.349353\pi$
$282$	−5289.53	+	5289.53i	−0.0665149	+	0.0665149i
$283$	84073.3	+	84073.3i	1.04975	+	1.04975i	0.998696	+	0.0510520i	$0.0162574\pi$
$283$	84073.3	+	84073.3i	1.04975	+	1.04975i	0.0510520	+	0.998696i	$0.483743\pi$
$284$			24777.1i			0.307194i
$285$	−1010.92			−0.0124460
$286$		−	19977.9i		−	0.244241i
$287$		−	90048.1i		−	1.09323i
$288$	2617.09	+	2617.09i	0.0315524	+	0.0315524i
$289$			83091.2i			0.994854i
$290$	128092.	+	128092.i	1.52309	+	1.52309i
$291$	−15774.8	−	15774.8i	−0.186284	−	0.186284i
$292$	19893.2			0.233313
$293$	−142984.			−1.66553			−0.832767	−	0.553624i	$-0.813245\pi$
$293$	−142984.			−1.66553			−0.832767	+	0.553624i	$0.813245\pi$
$294$	−17990.7	+	17990.7i	−0.208139	+	0.208139i
$295$		−	66073.7i		−	0.759249i
$296$	−30282.9	+	6520.40i	−0.345632	+	0.0744202i
$297$	14025.5			0.159003
$298$	−49123.9	−	49123.9i	−0.553172	−	0.553172i
$299$		−	506.490i		−	0.00566538i
$300$		−	77490.7i		−	0.861008i
$301$	−48107.5	+	48107.5i	−0.530982	+	0.530982i
$302$	−47500.6	+	47500.6i	−0.520817	+	0.520817i
$303$	69961.3			0.762031
$304$	114.030	−	114.030i	0.00123387	−	0.00123387i
$305$	−53378.5			−0.573808
$306$	−1198.86			−0.0128034
$307$		−	26098.0i		−	0.276905i	−0.990369	−	0.138453i	$-0.955787\pi$
$307$		−	26098.0i		−	0.276905i	0.990369	−	0.138453i	$-0.0442129\pi$
$308$	7143.88			0.0753065
$309$	98789.4	−	98789.4i	1.03465	−	1.03465i
$310$	−98639.3	−	98639.3i	−1.02642	−	1.02642i
$311$	−8716.65	−	8716.65i	−0.0901215	−	0.0901215i	0.660609	−	0.750730i	$-0.270298\pi$
$311$	−8716.65	−	8716.65i	−0.0901215	−	0.0901215i	−0.750730	+	0.660609i	$0.770298\pi$
$312$	−70000.3			−0.719102
$313$	−33292.4	+	33292.4i	−0.339826	+	0.339826i	−0.856302	−	0.516476i	$-0.827244\pi$
$313$	−33292.4	+	33292.4i	−0.339826	+	0.339826i	0.516476	+	0.856302i	$0.327244\pi$
$314$	−14972.5	−	14972.5i	−0.151857	−	0.151857i
$315$	−22362.9	+	22362.9i	−0.225375	+	0.225375i
$316$	−46617.5	−	46617.5i	−0.466848	−	0.466848i
$317$			15534.4i			0.154588i	0.997008	+	0.0772938i	$0.0246279\pi$
$317$			15534.4i			0.154588i	−0.997008	+	0.0772938i	$0.975372\pi$
$318$	−9634.92	+	9634.92i	−0.0952783	+	0.0952783i
$319$	26144.9	−	26144.9i	0.256925	−	0.256925i
$320$	14421.3	+	14421.3i	0.140833	+	0.140833i
$321$			223642.i			2.17042i
$322$	181.115			0.00174680
$323$			52.2358i			0.000500684i
$324$		−	62392.7i		−	0.594352i
$325$	208869.	+	208869.i	1.97746	+	1.97746i
$326$			1801.79i			0.0169539i
$327$	−5340.31	−	5340.31i	−0.0499425	−	0.0499425i
$328$	−37102.9	−	37102.9i	−0.344874	−	0.344874i
$329$	10196.6			0.0942028
$330$	−26095.7			−0.239630
$331$	−152803.	+	152803.i	−1.39468	+	1.39468i	−0.580220	+	0.814460i	$0.697033\pi$
$331$	−152803.	+	152803.i	−1.39468	+	1.39468i	−0.814460	+	0.580220i	$0.802967\pi$
$332$		−	80753.6i		−	0.732631i
$333$	−23515.0	−	15182.8i	−0.212059	−	0.136918i
$334$	18679.0			0.167440
$335$	−162013.	−	162013.i	−1.44364	−	1.44364i
$336$		−	25031.3i		−	0.221720i
$337$		−	107583.i		−	0.947289i	−0.880716	−	0.473644i	$-0.842938\pi$
$337$		−	107583.i		−	0.947289i	0.880716	−	0.473644i	$-0.157062\pi$
$338$	131557.	−	131557.i	1.15155	−	1.15155i
$339$	−103664.	+	103664.i	−0.902049	+	0.902049i
$340$	−6606.24			−0.0571474
$341$	−20133.3	+	20133.3i	−0.173143	+	0.173143i
$342$	145.715			0.00124581
$343$	127915.			1.08726
$344$			39643.9i			0.335011i
$345$	−661.591			−0.00555842
$346$	−78845.6	+	78845.6i	−0.658605	+	0.658605i
$347$	−36455.4	−	36455.4i	−0.302763	−	0.302763i	0.539331	−	0.842094i	$-0.318677\pi$
$347$	−36455.4	−	36455.4i	−0.302763	−	0.302763i	−0.842094	+	0.539331i	$0.818677\pi$
$348$	−91608.7	−	91608.7i	−0.756446	−	0.756446i
$349$	−34337.2			−0.281912			−0.140956	−	0.990016i	$-0.545018\pi$
$349$	−34337.2			−0.281912			−0.140956	+	0.990016i	$0.545018\pi$
$350$	−74689.3	+	74689.3i	−0.609709	+	0.609709i
$351$	132462.	+	132462.i	1.07517	+	1.07517i
$352$	2943.52	−	2943.52i	0.0237565	−	0.0237565i
$353$	−52895.0	−	52895.0i	−0.424488	−	0.424488i	0.462258	−	0.886746i	$-0.347039\pi$
$353$	−52895.0	−	52895.0i	−0.424488	−	0.424488i	−0.886746	+	0.462258i	$0.847039\pi$
$354$			47254.4i			0.377082i
$355$	−87235.5	+	87235.5i	−0.692208	+	0.692208i
$356$	−74525.8	+	74525.8i	−0.588040	+	0.588040i
$357$	5733.30	+	5733.30i	0.0449850	+	0.0449850i
$358$			72029.7i			0.562012i
$359$	76865.8			0.596409			0.298204	−	0.954502i	$-0.403612\pi$
$359$	76865.8			0.596409			0.298204	+	0.954502i	$0.403612\pi$
$360$			18428.6i			0.142196i
$361$			130315.i			0.999951i
$362$	57477.8	+	57477.8i	0.438614	+	0.438614i
$363$		−	142138.i		−	1.07869i
$364$	67469.7	+	67469.7i	0.509220	+	0.509220i
$365$	70040.4	+	70040.4i	0.525730	+	0.525730i
$366$	38175.2			0.284983
$367$	−45037.2			−0.334379			−0.167190	−	0.985925i	$-0.553469\pi$
$367$	−45037.2			−0.334379			−0.167190	+	0.985925i	$0.553469\pi$
$368$	74.6258	−	74.6258i	0.000551053	−	0.000551053i
$369$		−	47412.9i		−	0.348212i
$370$	−129578.	−	83663.4i	−0.946513	−	0.611128i
$371$	18573.2			0.134939
$372$	70544.7	+	70544.7i	0.509775	+	0.509775i
$373$		−	157740.i		−	1.13377i	−0.823798	−	0.566884i	$-0.808149\pi$
$373$		−	157740.i		−	1.13377i	0.823798	−	0.566884i	$-0.191851\pi$
$374$			1348.40i			0.00963996i
$375$	95521.6	−	95521.6i	0.679264	−	0.679264i
$376$	4201.36	−	4201.36i	0.0297176	−	0.0297176i
$377$	493846.			3.47463
$378$	−47367.1	+	47367.1i	−0.331507	+	0.331507i
$379$	126871.			0.883254			0.441627	−	0.897199i	$-0.354402\pi$
$379$	126871.			0.883254			0.441627	+	0.897199i	$0.354402\pi$
$380$	802.954			0.00556062
$381$			93864.7i			0.646625i
$382$	151164.			1.03591
$383$	−81269.3	+	81269.3i	−0.554024	+	0.554024i	−0.927600	−	0.373575i	$-0.878132\pi$
$383$	−81269.3	+	81269.3i	−0.554024	+	0.554024i	0.373575	+	0.927600i	$0.378132\pi$
$384$	−10313.8	−	10313.8i	−0.0699447	−	0.0699447i
$385$	25152.3	+	25152.3i	0.169690	+	0.169690i
$386$	162969.			1.09378
$387$	−25330.0	+	25330.0i	−0.169127	+	0.169127i
$388$	12529.5	+	12529.5i	0.0832284	+	0.0832284i
$389$	44070.5	−	44070.5i	0.291238	−	0.291238i	−0.546331	−	0.837569i	$-0.683976\pi$
$389$	44070.5	−	44070.5i	0.291238	−	0.291238i	0.837569	+	0.546331i	$0.183976\pi$
$390$	−246458.	−	246458.i	−1.62037	−	1.62037i
$391$			34.1853i			0.000223607i
$392$	14289.6	−	14289.6i	0.0929925	−	0.0929925i
$393$	142946.	−	142946.i	0.925525	−	0.925525i
$394$	−138454.	−	138454.i	−0.891892	−	0.891892i
$395$		−	328263.i		−	2.10392i
$396$	3761.45			0.0239864
$397$			130110.i			0.825521i	0.910840	+	0.412760i	$0.135435\pi$
$397$			130110.i			0.825521i	−0.910840	+	0.412760i	$0.864565\pi$
$398$			139138.i			0.878375i
$399$	−696.853	−	696.853i	−0.00437719	−	0.00437719i
$400$			61549.2i			0.384682i
$401$	4058.65	+	4058.65i	0.0252402	+	0.0252402i	0.719614	−	0.694374i	$-0.244319\pi$
$401$	4058.65	+	4058.65i	0.0252402	+	0.0252402i	−0.694374	+	0.719614i	$0.744319\pi$
$402$	115868.	+	115868.i	0.716987	+	0.716987i
$403$	−380294.			−2.34158
$404$	−55568.7			−0.340461
$405$	219673.	−	219673.i	1.33927	−	1.33927i
$406$			176594.i			1.07133i
$407$	−17076.6	+	26448.1i	−0.103089	+	0.159664i
$408$	4724.64			0.0283823
$409$	58146.1	+	58146.1i	0.347595	+	0.347595i	0.859213	−	0.511618i	$-0.170954\pi$
$409$	58146.1	+	58146.1i	0.347595	+	0.347595i	−0.511618	+	0.859213i	$0.670954\pi$
$410$		−	261265.i		−	1.55423i
$411$		−	48915.4i		−	0.289576i
$412$	−78466.3	+	78466.3i	−0.462263	+	0.462263i
$413$	45546.1	−	45546.1i	0.267025	−	0.267025i
$414$	95.3623			0.000556386
$415$	284318.	−	284318.i	1.65085	−	1.65085i
$416$	55599.7			0.321281
$417$	−323371.			−1.85964
$418$		−	163.891i		−	0.000938000i
$419$	137017.			0.780451			0.390225	−	0.920719i	$-0.372397\pi$
$419$	137017.			0.780451			0.390225	+	0.920719i	$0.372397\pi$
$420$	88130.6	−	88130.6i	0.499607	−	0.499607i
$421$	−42860.2	−	42860.2i	−0.241819	−	0.241819i	0.575783	−	0.817602i	$-0.304697\pi$
$421$	−42860.2	−	42860.2i	−0.241819	−	0.241819i	−0.817602	+	0.575783i	$0.804697\pi$
$422$	30364.8	+	30364.8i	0.170508	+	0.170508i
$423$	5368.80			0.0300052
$424$	7652.81	−	7652.81i	0.0425686	−	0.0425686i
$425$	−14097.5	−	14097.5i	−0.0780486	−	0.0780486i
$426$	62388.9	−	62388.9i	0.343786	−	0.343786i
$427$	−36795.1	−	36795.1i	−0.201806	−	0.201806i
$428$		−	177634.i		−	0.969702i
$429$	−50304.6	+	50304.6i	−0.273334	+	0.273334i
$430$	−139579.	+	139579.i	−0.754889	+	0.754889i
$431$	227199.	+	227199.i	1.22307	+	1.22307i	0.966534	+	0.256537i	$0.0825814\pi$
$431$	227199.	+	227199.i	1.22307	+	1.22307i	0.256537	+	0.966534i	$0.417419\pi$
$432$			39033.8i			0.209157i
$433$	−283947.			−1.51447			−0.757236	−	0.653142i	$-0.773451\pi$
$433$	−283947.			−1.51447			−0.757236	+	0.653142i	$0.773451\pi$
$434$		−	135989.i		−	0.721977i
$435$		−	645074.i		−	3.40903i
$436$	4241.69	+	4241.69i	0.0223134	+	0.0223134i
$437$		−	4.15505i		−	2.17577e-5i
$438$	−50091.3	−	50091.3i	−0.261105	−	0.261105i
$439$	216787.	+	216787.i	1.12488	+	1.12488i	0.990998	+	0.133878i	$0.0427432\pi$
$439$	216787.	+	216787.i	1.12488	+	1.12488i	0.133878	+	0.990998i	$0.457257\pi$
$440$	20727.2			0.107062
$441$	18260.3			0.0938926
$442$	−12734.8	+	12734.8i	−0.0651851	+	0.0651851i
$443$			150902.i			0.768933i	0.923139	+	0.384467i	$0.125615\pi$
$443$			150902.i			0.768933i	−0.923139	+	0.384467i	$0.874385\pi$
$444$	92671.1	+	59834.3i	0.470087	+	0.303518i
$445$	−524783.			−2.65009
$446$	−89703.3	−	89703.3i	−0.450961	−	0.450961i
$447$			247389.i			1.23813i
$448$			19881.8i			0.0990604i
$449$	−144221.	+	144221.i	−0.715381	+	0.715381i	−0.967656	−	0.252275i	$-0.918821\pi$
$449$	−144221.	+	144221.i	−0.715381	+	0.715381i	0.252275	+	0.967656i	$0.418821\pi$
$450$	−39326.1	+	39326.1i	−0.194203	+	0.194203i
$451$	−53326.9			−0.262176
$452$	82338.3	−	82338.3i	0.403019	−	0.403019i
$453$	239214.			1.16571
$454$	107994.			0.523947
$455$			475096.i			2.29487i
$456$	−574.255			−0.00276169
$457$	−53789.8	+	53789.8i	−0.257553	+	0.257553i	−0.824058	−	0.566505i	$-0.808295\pi$
$457$	−53789.8	+	53789.8i	−0.257553	+	0.257553i	0.566505	+	0.824058i	$0.308295\pi$
$458$	88623.1	+	88623.1i	0.422489	+	0.422489i
$459$	−8940.49	−	8940.49i	−0.0424361	−	0.0424361i
$460$	525.487			0.00248340
$461$	−68360.8	+	68360.8i	−0.321666	+	0.321666i	−0.849406	−	0.527740i	$-0.823040\pi$
$461$	−68360.8	+	68360.8i	−0.321666	+	0.321666i	0.527740	+	0.849406i	$0.323040\pi$
$462$	−17988.4	−	17988.4i	−0.0842767	−	0.0842767i
$463$	−38373.6	+	38373.6i	−0.179007	+	0.179007i	−0.790923	−	0.611916i	$-0.790399\pi$
$463$	−38373.6	+	38373.6i	−0.179007	+	0.179007i	0.611916	+	0.790923i	$0.290399\pi$
$464$	72762.8	+	72762.8i	0.337966	+	0.337966i
$465$			496750.i			2.29737i
$466$	143397.	−	143397.i	0.660340	−	0.660340i
$467$	120431.	−	120431.i	0.552210	−	0.552210i	−0.374868	−	0.927078i	$-0.622312\pi$
$467$	120431.	−	120431.i	0.552210	−	0.552210i	0.927078	+	0.374868i	$0.122312\pi$
$468$	35524.7	+	35524.7i	0.162195	+	0.162195i
$469$		−	223358.i		−	1.01544i
$470$	29584.4			0.133927
$471$			75402.0i			0.339892i
$472$		−	37533.2i		−	0.168473i
$473$	28489.5	+	28489.5i	0.127339	+	0.127339i
$474$			234767.i			1.04491i
$475$	1713.48	+	1713.48i	0.00759438	+	0.00759438i
$476$	−4553.83	−	4553.83i	−0.0200985	−	0.0200985i
$477$	9779.32			0.0429806
$478$	136630.			0.597985
$479$	187183.	−	187183.i	0.815820	−	0.815820i	−0.169679	−	0.985499i	$-0.554273\pi$
$479$	187183.	−	187183.i	0.815820	−	0.815820i	0.985499	+	0.169679i	$0.0542732\pi$
$480$		−	72625.7i		−	0.315216i
$481$	−411064.	+	88508.8i	−1.77672	+	0.382557i
$482$	32888.8			0.141564
$483$	−456.050	−	456.050i	−0.00195487	−	0.00195487i
$484$			112897.i			0.481940i
$485$			88228.4i			0.375081i
$486$	−58301.2	+	58301.2i	−0.246834	+	0.246834i
$487$	−175963.	+	175963.i	−0.741932	+	0.741932i	−0.972950	−	0.231018i	$-0.925795\pi$
$487$	−175963.	+	175963.i	−0.741932	+	0.741932i	0.231018	+	0.972950i	$0.425795\pi$
$488$	−30321.7			−0.127325
$489$	4536.92	−	4536.92i	0.0189733	−	0.0189733i
$490$	100622.			0.419084
$491$	−43433.7			−0.180162			−0.0900811	−	0.995934i	$-0.528713\pi$
$491$	−43433.7			−0.180162			−0.0900811	+	0.995934i	$0.528713\pi$
$492$			186851.i			0.771908i
$493$	−33331.9			−0.137141
$494$	1547.85	−	1547.85i	0.00634272	−	0.00634272i
$495$	13243.4	+	13243.4i	0.0540491	+	0.0540491i
$496$	−56032.1	−	56032.1i	−0.227758	−	0.227758i
$497$	−120267.			−0.486893
$498$	−203338.	+	203338.i	−0.819899	+	0.819899i
$499$	−300660.	−	300660.i	−1.20747	−	1.20747i	−0.971845	−	0.235622i	$-0.924287\pi$
$499$	−300660.	−	300660.i	−1.20747	−	1.20747i	−0.235622	−	0.971845i	$-0.575713\pi$
$500$	−75870.7	+	75870.7i	−0.303483	+	0.303483i
$501$	−47033.9	−	47033.9i	−0.187385	−	0.187385i
$502$			12472.6i			0.0494935i
$503$	−15729.9	+	15729.9i	−0.0621714	+	0.0621714i	−0.737509	−	0.675337i	$-0.763998\pi$
$503$	−15729.9	+	15729.9i	−0.0621714	+	0.0621714i	0.675337	+	0.737509i	$0.263998\pi$
$504$	−12703.2	+	12703.2i	−0.0500096	+	0.0500096i
$505$	−195647.	−	195647.i	−0.767169	−	0.767169i
$506$		−	107.257i		−	0.000418915i
$507$	−662526.			−2.57743
$508$		−	74554.7i		−	0.288900i
$509$		−	286098.i		−	1.10428i	−0.833751	−	0.552141i	$-0.813811\pi$
$509$		−	286098.i		−	1.10428i	0.833751	−	0.552141i	$-0.186189\pi$
$510$	16634.6	+	16634.6i	0.0639545	+	0.0639545i
$511$			96560.9i			0.369794i
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	1086.67	+	1086.67i	0.00412917	+	0.00412917i
$514$	−163132.			−0.617465
$515$	−552531.			−2.08325
$516$	99823.8	−	99823.8i	0.374916	−	0.374916i
$517$		−	6038.47i		−	0.0225916i
$518$	−31649.8	−	146992.i	−0.117953	−	0.547816i
$519$	397068.			1.47411
$520$	195756.	+	195756.i	0.723950	+	0.723950i
$521$			96804.5i			0.356632i	0.983973	+	0.178316i	$0.0570649\pi$
$521$			96804.5i			0.356632i	−0.983973	+	0.178316i	$0.942935\pi$
$522$			92981.6i			0.341237i
$523$	65703.6	−	65703.6i	0.240207	−	0.240207i	−0.576729	−	0.816936i	$-0.695671\pi$
$523$	65703.6	−	65703.6i	0.240207	−	0.240207i	0.816936	+	0.576729i	$0.195671\pi$
$524$	−113539.	+	113539.i	−0.413507	+	0.413507i
$525$	376137.			1.36467
$526$	264528.	−	264528.i	0.956094	−	0.956094i
$527$	25667.7			0.0924201
$528$	−14823.6			−0.0531725
$529$			279838.i			0.999990i
$530$	53888.2			0.191841
$531$	23981.3	−	23981.3i	0.0850519	−	0.0850519i
$532$	553.495	+	553.495i	0.00195565	+	0.00195565i
$533$	−503641.	−	503641.i	−1.77283	−	1.77283i
$534$	375313.			1.31617
$535$	625416.	−	625416.i	2.18505	−	2.18505i
$536$	−92031.4	−	92031.4i	−0.320336	−	0.320336i
$537$	181372.	−	181372.i	0.628957	−	0.628957i
$538$	−226818.	−	226818.i	−0.783632	−	0.783632i
$539$		−	20538.0i		−	0.0706937i
$540$	−137431.	+	137431.i	−0.471299	+	0.471299i
$541$	−140158.	+	140158.i	−0.478878	+	0.478878i	−0.904773	−	0.425895i	$-0.859959\pi$
$541$	−140158.	+	140158.i	−0.478878	+	0.478878i	0.425895	+	0.904773i	$0.359959\pi$
$542$	−94400.0	−	94400.0i	−0.321346	−	0.321346i
$543$		−	289459.i		−	0.981721i
$544$	−3752.67			−0.0126807
$545$			29868.4i			0.100559i
$546$		−	339779.i		−	1.13975i
$547$	320971.	+	320971.i	1.07273	+	1.07273i	0.997139	+	0.0755914i	$0.0240845\pi$
$547$	320971.	+	320971.i	1.07273	+	1.07273i	0.0755914	+	0.997139i	$0.475916\pi$
$548$			38852.4i			0.129377i
$549$	−19373.6	−	19373.6i	−0.0642786	−	0.0642786i
$550$	44231.3	+	44231.3i	0.146219	+	0.146219i
$551$	4051.32			0.0133442
$552$	−375.817			−0.00123338
$553$	226280.	−	226280.i	0.739938	−	0.739938i
$554$			169204.i			0.551303i
$555$	115612.	+	536943.i	0.375335	+	1.74318i
$556$	256846.			0.830852
$557$	−93573.9	−	93573.9i	−0.301609	−	0.301609i	0.540034	−	0.841643i	$-0.318411\pi$
$557$	−93573.9	−	93573.9i	−0.301609	−	0.301609i	−0.841643	+	0.540034i	$0.818411\pi$
$558$		−	71602.0i		−	0.229962i
$559$			538132.i			1.72213i
$560$	−70000.2	+	70000.2i	−0.223215	+	0.223215i
$561$	3395.28	−	3395.28i	0.0107882	−	0.0107882i
$562$	−137165.			−0.434280
$563$	−352009.	+	352009.i	−1.11055	+	1.11055i	−0.117471	+	0.993076i	$0.537479\pi$
$563$	−352009.	+	352009.i	−1.11055	+	1.11055i	−0.993076	+	0.117471i	$0.962521\pi$
$564$	−21158.1			−0.0665149
$565$	579796.			1.81626
$566$			336293.i			1.04975i
$567$	302852.			0.942028
$568$	−49554.1	+	49554.1i	−0.153597	+	0.153597i
$569$	14681.9	+	14681.9i	0.0453481	+	0.0453481i	0.729417	−	0.684069i	$-0.239791\pi$
$569$	14681.9	+	14681.9i	0.0453481	+	0.0453481i	−0.684069	+	0.729417i	$0.739791\pi$
$570$	−2021.85	−	2021.85i	−0.00622298	−	0.00622298i
$571$	589695.			1.80865			0.904327	−	0.426840i	$-0.140373\pi$
$571$	589695.			1.80865			0.904327	+	0.426840i	$0.140373\pi$
$572$	39955.8	−	39955.8i	0.122120	−	0.122120i
$573$	−380633.	−	380633.i	−1.15930	−	1.15930i
$574$	180096.	−	180096.i	0.546614	−	0.546614i
$575$	1121.38	+	1121.38i	0.00339168	+	0.00339168i
$576$			10468.3i			0.0315524i
$577$	284270.	−	284270.i	0.853846	−	0.853846i	−0.136759	−	0.990604i	$-0.543668\pi$
$577$	284270.	−	284270.i	0.853846	−	0.853846i	0.990604	+	0.136759i	$0.0436685\pi$
$578$	−166182.	+	166182.i	−0.497427	+	0.497427i
$579$	−410359.	−	410359.i	−1.22407	−	1.22407i
$580$			512368.i			1.52309i
$581$	391975.			1.16120
$582$		−	63099.0i		−	0.186284i
$583$		−	10999.1i		−	0.0323610i
$584$	39786.5	+	39786.5i	0.116657	+	0.116657i
$585$			250152.i			0.730957i
$586$	−285969.	−	285969.i	−0.832767	−	0.832767i
$587$	−98954.1	−	98954.1i	−0.287182	−	0.287182i	0.548783	−	0.835965i	$-0.315091\pi$
$587$	−98954.1	−	98954.1i	−0.287182	−	0.287182i	−0.835965	+	0.548783i	$0.815091\pi$
$588$	−71962.7			−0.208139
$589$	−3119.78			−0.00899278
$590$	132147.	−	132147.i	0.379625	−	0.379625i
$591$			697256.i			1.99626i
$592$	−73606.6	−	47525.0i	−0.210026	−	0.135606i
$593$	17570.1			0.0499649			0.0249824	−	0.999688i	$-0.492047\pi$
$593$	17570.1			0.0499649			0.0249824	+	0.999688i	$0.492047\pi$
$594$	28051.0	+	28051.0i	0.0795015	+	0.0795015i
$595$		−	32066.4i		−	0.0905767i
$596$		−	196496.i		−	0.553172i
$597$	350351.	−	350351.i	0.983004	−	0.983004i
$598$	1012.98	−	1012.98i	0.00283269	−	0.00283269i
$599$	468604.			1.30603			0.653014	−	0.757346i	$-0.273504\pi$
$599$	468604.			1.30603			0.653014	+	0.757346i	$0.273504\pi$
$600$	154981.	−	154981.i	0.430504	−	0.430504i
$601$	−70719.2			−0.195789			−0.0978946	−	0.995197i	$-0.531211\pi$
$601$	−70719.2			−0.195789			−0.0978946	+	0.995197i	$0.531211\pi$
$602$	−192430.			−0.530982
$603$		−	117604.i		−	0.323437i
$604$	−190002.			−0.520817
$605$	−397491.	+	397491.i	−1.08597	+	1.08597i
$606$	139923.	+	139923.i	0.381016	+	0.381016i
$607$	123076.	+	123076.i	0.334038	+	0.334038i	0.854118	−	0.520080i	$-0.174098\pi$
$607$	123076.	+	123076.i	0.334038	+	0.334038i	−0.520080	+	0.854118i	$0.674098\pi$
$608$	456.118			0.00123387
$609$	444665.	−	444665.i	1.19894	−	1.19894i
$610$	−106757.	−	106757.i	−0.286904	−	0.286904i
$611$	57029.8	−	57029.8i	0.152763	−	0.152763i
$612$	−2397.72	−	2397.72i	−0.00640171	−	0.00640171i
$613$			91520.8i			0.243556i	0.992557	+	0.121778i	$0.0388596\pi$
$613$			91520.8i			0.243556i	−0.992557	+	0.121778i	$0.961140\pi$
$614$	52196.1	−	52196.1i	0.138453	−	0.138453i
$615$	−657868.	+	657868.i	−1.73936	+	1.73936i
$616$	14287.8	+	14287.8i	0.0376533	+	0.0376533i
$617$			214751.i			0.564111i	0.959398	+	0.282056i	$0.0910163\pi$
$617$			214751.i			0.564111i	−0.959398	+	0.282056i	$0.908984\pi$
$618$	395158.			1.03465
$619$			76674.2i			0.200110i	0.994982	+	0.100055i	$0.0319018\pi$
$619$			76674.2i			0.200110i	−0.994982	+	0.100055i	$0.968098\pi$
$620$		−	394557.i		−	1.02642i
$621$	711.163	+	711.163i	0.00184411	+	0.00184411i
$622$		−	34866.6i		−	0.0901215i
$623$	−361745.	−	361745.i	−0.932023	−	0.932023i
$624$	−140001.	−	140001.i	−0.359551	−	0.359551i
$625$	66812.9			0.171041
$626$	−133170.			−0.339826
$627$	−412.679	+	412.679i	−0.00104973	+	0.00104973i
$628$		−	59890.1i		−	0.151857i
$629$	27744.6	−	5973.86i	0.0701257	−	0.0150992i
$630$	−89451.5			−0.225375
$631$	−236291.	−	236291.i	−0.593456	−	0.593456i	0.345107	−	0.938563i	$-0.387843\pi$
$631$	−236291.	−	236291.i	−0.593456	−	0.593456i	−0.938563	+	0.345107i	$0.887843\pi$
$632$		−	186470.i		−	0.466848i
$633$		−	152918.i		−	0.381637i
$634$	−31068.7	+	31068.7i	−0.0772938	+	0.0772938i
$635$	262493.	−	262493.i	0.650985	−	0.650985i
$636$	−38539.7			−0.0952783
$637$	193969.	−	193969.i	0.478028	−	0.478028i
$638$	104580.			0.256925
$639$	−63323.9			−0.155084
$640$			57685.0i			0.140833i
$641$	665803.			1.62043			0.810214	−	0.586134i	$-0.199351\pi$
$641$	665803.			1.62043			0.810214	+	0.586134i	$0.199351\pi$
$642$	−447284.	+	447284.i	−1.08521	+	1.08521i
$643$	−170519.	−	170519.i	−0.412431	−	0.412431i	0.470154	−	0.882584i	$-0.344198\pi$
$643$	−170519.	−	170519.i	−0.412431	−	0.412431i	−0.882584	+	0.470154i	$0.844198\pi$
$644$	362.230	+	362.230i	0.000873400	+	0.000873400i
$645$	702922.			1.68961
$646$	−104.472	+	104.472i	−0.000250342	+	0.000250342i
$647$	−77581.9	−	77581.9i	−0.185333	−	0.185333i	0.608342	−	0.793675i	$-0.291835\pi$
$647$	−77581.9	−	77581.9i	−0.185333	−	0.185333i	−0.793675	+	0.608342i	$0.791835\pi$
$648$	124785.	−	124785.i	0.297176	−	0.297176i
$649$	−26972.6	−	26972.6i	−0.0640374	−	0.0640374i
$650$			835477.i			1.97746i
$651$	−342421.	+	342421.i	−0.807976	+	0.807976i
$652$	−3603.58	+	3603.58i	−0.00847694	+	0.00847694i
$653$	237385.	+	237385.i	0.556708	+	0.556708i	0.928369	−	0.371661i	$-0.121212\pi$
$653$	237385.	+	237385.i	0.556708	+	0.556708i	−0.371661	+	0.928369i	$0.621212\pi$
$654$		−	21361.2i		−	0.0499425i
$655$	−799501.			−1.86353
$656$		−	148412.i		−	0.344874i
$657$			50842.1i			0.117786i
$658$	20393.2	+	20393.2i	0.0471014	+	0.0471014i
$659$			401978.i			0.925616i	0.886458	+	0.462808i	$0.153158\pi$
$659$			401978.i			0.925616i	−0.886458	+	0.462808i	$0.846842\pi$
$660$	−52191.3	−	52191.3i	−0.119815	−	0.119815i
$661$	−237599.	−	237599.i	−0.543804	−	0.543804i	0.380838	−	0.924642i	$-0.375636\pi$
$661$	−237599.	−	237599.i	−0.543804	−	0.543804i	−0.924642	+	0.380838i	$0.875636\pi$
$662$	−611210.			−1.39468
$663$	64132.9			0.145899
$664$	161507.	−	161507.i	0.366316	−	0.366316i
$665$			3897.51i			0.00881340i
$666$	−16664.5	−	77395.5i	−0.0375702	−	0.174489i
$667$	2651.36			0.00595959
$668$	37358.0	+	37358.0i	0.0837202	+	0.0837202i
$669$			451748.i			1.00935i
$670$		−	648051.i		−	1.44364i
$671$	−21790.2	+	21790.2i	−0.0483967	+	0.0483967i
$672$	50062.6	−	50062.6i	0.110860	−	0.110860i
$673$	713482.			1.57526			0.787631	−	0.616147i	$-0.211307\pi$
$673$	713482.			1.57526			0.787631	+	0.616147i	$0.211307\pi$
$674$	215165.	−	215165.i	0.473644	−	0.473644i
$675$	−586547.			−1.28735
$676$	526230.			1.15155
$677$			26389.7i			0.0575781i	0.999586	+	0.0287890i	$0.00916510\pi$
$677$			26389.7i			0.0575781i	−0.999586	+	0.0287890i	$0.990835\pi$
$678$	−414658.			−0.902049
$679$	−60817.9	+	60817.9i	−0.131914	+	0.131914i
$680$	−13212.5	−	13212.5i	−0.0285737	−	0.0285737i
$681$	−271930.	−	271930.i	−0.586358	−	0.586358i
$682$	−80533.1			−0.173143
$683$	−29972.1	+	29972.1i	−0.0642505	+	0.0642505i	−0.738502	−	0.674251i	$-0.764466\pi$
$683$	−29972.1	+	29972.1i	−0.0642505	+	0.0642505i	0.674251	+	0.738502i	$0.264466\pi$
$684$	291.431	+	291.431i	0.000622907	+	0.000622907i
$685$	−136792.	+	136792.i	−0.291528	+	0.291528i
$686$	255831.	+	255831.i	0.543632	+	0.543632i
$687$		−	446308.i		−	0.945629i
$688$	−79287.8	+	79287.8i	−0.167506	+	0.167506i
$689$	103880.	−	103880.i	0.218824	−	0.218824i
$690$	−1323.18	−	1323.18i	−0.00277921	−	0.00277921i
$691$			746666.i			1.56376i	0.623428	+	0.781881i	$0.285739\pi$
$691$			746666.i			1.56376i	−0.623428	+	0.781881i	$0.714261\pi$
$692$	−315382.			−0.658605
$693$			18257.9i			0.0380177i
$694$		−	145822.i		−	0.302763i
$695$	904309.	+	904309.i	1.87218	+	1.87218i
$696$		−	366435.i		−	0.756446i
$697$	33993.0	+	33993.0i	0.0699719	+	0.0699719i
$698$	−68674.3	−	68674.3i	−0.140956	−	0.140956i
$699$	−722150.			−1.47799
$700$	−298757.			−0.609709
$701$	271675.	−	271675.i	0.552857	−	0.552857i	−0.374407	−	0.927264i	$-0.622154\pi$
$701$	271675.	−	271675.i	0.552857	−	0.552857i	0.927264	+	0.374407i	$0.122154\pi$
$702$			529850.i			1.07517i
$703$	−3372.21	+	726.092i	−0.00682346	+	0.00146920i
$704$	11774.1			0.0237565
$705$	−74493.8	−	74493.8i	−0.149879	−	0.149879i
$706$		−	211580.i		−	0.424488i
$707$		−	269728.i		−	0.539620i
$708$	−94508.9	+	94508.9i	−0.188541	+	0.188541i
$709$	−89230.7	+	89230.7i	−0.177510	+	0.177510i	−0.790269	−	0.612760i	$-0.790059\pi$
$709$	−89230.7	+	89230.7i	−0.177510	+	0.177510i	0.612760	+	0.790269i	$0.290059\pi$
$710$	−348942.			−0.692208
$711$	119143.	−	119143.i	0.235683	−	0.235683i
$712$	−298103.			−0.588040
$713$	−2041.72			−0.00401621
$714$			22933.2i			0.0449850i
$715$	281354.			0.550353
$716$	−144059.	+	144059.i	−0.281006	+	0.281006i
$717$	−344036.	−	344036.i	−0.669214	−	0.669214i
$718$	153732.	+	153732.i	0.298204	+	0.298204i
$719$	−9096.39			−0.0175959			−0.00879795	−	0.999961i	$-0.502801\pi$
$719$	−9096.39			−0.0175959			−0.00879795	+	0.999961i	$0.502801\pi$
$720$	−36857.1	+	36857.1i	−0.0710978	+	0.0710978i
$721$	−380872.	−	380872.i	−0.732671	−	0.732671i
$722$	−260629.	+	260629.i	−0.499976	+	0.499976i
$723$	−82814.3	−	82814.3i	−0.158427	−	0.158427i
$724$			229911.i			0.438614i
$725$	−1.09338e6	+	1.09338e6i	−2.08015	+	2.08015i
$726$	284277.	−	284277.i	0.539347	−	0.539347i
$727$	544278.	+	544278.i	1.02980	+	1.02980i	0.999542	+	0.0302551i	$0.00963196\pi$
$727$	544278.	+	544278.i	1.02980	+	1.02980i	0.0302551	+	0.999542i	$0.490368\pi$
$728$			269879.i			0.509220i
$729$	−338120.			−0.636232
$730$			280162.i			0.525730i
$731$		−	36321.0i		−	0.0679708i
$732$	76350.3	+	76350.3i	0.142491	+	0.142491i
$733$		−	659872.i		−	1.22815i	−0.789247	−	0.614076i	$-0.789529\pi$
$733$		−	659872.i		−	1.22815i	0.789247	−	0.614076i	$-0.210471\pi$
$734$	−90074.4	−	90074.4i	−0.167190	−	0.167190i
$735$	−253368.	−	253368.i	−0.469004	−	0.469004i
$736$	298.503			0.000551053
$737$	−132274.			−0.243522
$738$	94825.8	−	94825.8i	0.174106	−	0.174106i
$739$			521481.i			0.954881i	0.878664	+	0.477441i	$0.158435\pi$
$739$			521481.i			0.954881i	−0.878664	+	0.477441i	$0.841565\pi$
$740$	−91828.5	−	426482.i	−0.167693	−	0.778821i
$741$	−7795.02			−0.0141965
$742$	37146.4	+	37146.4i	0.0674697	+	0.0674697i
$743$			16416.7i			0.0297378i	0.999889	+	0.0148689i	$0.00473310\pi$
$743$			16416.7i			0.0297378i	−0.999889	+	0.0148689i	$0.995267\pi$
$744$			282179.i			0.509775i
$745$	691825.	−	691825.i	1.24647	−	1.24647i
$746$	315480.	−	315480.i	0.566884	−	0.566884i
$747$	206386.			0.369861
$748$	−2696.80	+	2696.80i	−0.00481998	+	0.00481998i
$749$	862228.			1.53695
$750$	382086.			0.679264
$751$		−	999787.i		−	1.77267i	−0.463045	−	0.886335i	$-0.653243\pi$
$751$		−	999787.i		−	1.77267i	0.463045	−	0.886335i	$-0.346757\pi$
$752$	16805.4			0.0297176
$753$	31406.0	−	31406.0i	0.0553889	−	0.0553889i
$754$	987692.	+	987692.i	1.73732	+	1.73732i
$755$	−668963.	−	668963.i	−1.17357	−	1.17357i
$756$	−189468.			−0.331507
$757$	−245928.	+	245928.i	−0.429158	+	0.429158i	−0.888341	−	0.459184i	$-0.848142\pi$
$757$	−245928.	+	245928.i	−0.429158	+	0.429158i	0.459184	+	0.888341i	$0.348142\pi$
$758$	253743.	+	253743.i	0.441627	+	0.441627i
$759$	−270.075	+	270.075i	−0.000468814	+	0.000468814i
$760$	1605.91	+	1605.91i	0.00278031	+	0.00278031i
$761$			532524.i			0.919539i	0.888038	+	0.459769i	$0.152068\pi$
$761$			532524.i			0.919539i	−0.888038	+	0.459769i	$0.847932\pi$
$762$	−187729.	+	187729.i	−0.323312	+	0.323312i
$763$	−20589.0	+	20589.0i	−0.0353660	+	0.0353660i
$764$	302328.	+	302328.i	0.517955	+	0.517955i
$765$		−	16883.9i		−	0.0288502i
$766$	−325077.			−0.554024
$767$		−	509480.i		−	0.866037i
$768$		−	41255.1i		−	0.0699447i
$769$	−496806.	−	496806.i	−0.840106	−	0.840106i	0.148766	−	0.988872i	$-0.452470\pi$
$769$	−496806.	−	496806.i	−0.840106	−	0.840106i	−0.988872	+	0.148766i	$0.952470\pi$
$770$			100609.i			0.169690i
$771$	410767.	+	410767.i	0.691014	+	0.691014i
$772$	325939.	+	325939.i	0.546892	+	0.546892i
$773$	−475443.			−0.795681			−0.397841	−	0.917455i	$-0.630240\pi$
$773$	−475443.			−0.795681			−0.397841	+	0.917455i	$0.630240\pi$
$774$	−101320.			−0.169127
$775$	841975.	−	841975.i	1.40183	−	1.40183i
$776$			50118.2i			0.0832284i
$777$	−290433.	+	449822.i	−0.481065	+	0.745072i
$778$	176282.			0.291238
$779$	−4131.67	−	4131.67i	−0.00680849	−	0.00680849i
$780$		−	985832.i		−	1.62037i
$781$			71222.6i			0.116766i
$782$	−68.3706	+	68.3706i	−0.000111804	+	0.000111804i
$783$	−693409.	+	693409.i	−1.13101	+	1.13101i
$784$	57158.4			0.0929925
$785$	210862.	−	210862.i	0.342184	−	0.342184i
$786$	571785.			0.925525
$787$	172211.			0.278043			0.139021	−	0.990289i	$-0.455604\pi$
$787$	172211.			0.278043			0.139021	+	0.990289i	$0.455604\pi$
$788$		−	553815.i		−	0.891892i
$789$	−1.33217e6			−2.13996
$790$	656527.	−	656527.i	1.05196	−	1.05196i
$791$	399667.	+	399667.i	0.638771	+	0.638771i
$792$	7522.91	+	7522.91i	0.0119932	+	0.0119932i
$793$	−411591.			−0.654515
$794$	−260219.	+	260219.i	−0.412760	+	0.412760i
$795$	−135691.	−	135691.i	−0.214693	−	0.214693i
$796$	−278276.	+	278276.i	−0.439188	+	0.439188i
$797$	−268309.	−	268309.i	−0.422394	−	0.422394i	0.463633	−	0.886027i	$-0.346546\pi$
$797$	−268309.	−	268309.i	−0.422394	−	0.422394i	−0.886027	+	0.463633i	$0.846546\pi$
$798$		−	2787.41i		−	0.00437719i
$799$	−3849.20	+	3849.20i	−0.00602944	+	0.00602944i
$800$	−123098.	+	123098.i	−0.192341	+	0.192341i
$801$	−190469.	−	190469.i	−0.296865	−	0.296865i
$802$			16234.6i			0.0252402i
$803$	57183.8			0.0886833
$804$			463472.i			0.716987i
$805$			2550.69i			0.00393610i
$806$	−760587.	−	760587.i	−1.17079	−	1.17079i
$807$			1.14226e6i			1.75395i
$808$	−111137.	−	111137.i	−0.170231	−	0.170231i
$809$	−815207.	−	815207.i	−1.24558	−	1.24558i	−0.957653	−	0.287926i	$-0.907034\pi$
$809$	−815207.	−	815207.i	−1.24558	−	1.24558i	−0.287926	−	0.957653i	$-0.592966\pi$
$810$	878693.			1.33927
$811$	404145.			0.614462			0.307231	−	0.951635i	$-0.400598\pi$
$811$	404145.			0.614462			0.307231	+	0.951635i	$0.400598\pi$
$812$	−353188.	+	353188.i	−0.535665	+	0.535665i
$813$			475400.i			0.719247i
$814$	−87049.3	+	18743.1i	−0.131376	+	0.0282874i
$815$	−25375.1			−0.0382025
$816$	9449.27	+	9449.27i	0.0141912	+	0.0141912i
$817$			4414.63i			0.00661378i
$818$			232584.i			0.347595i
$819$	−172435.	+	172435.i	−0.257074	+	0.257074i
$820$	522530.	−	522530.i	0.777113	−	0.777113i
$821$	619988.			0.919807			0.459903	−	0.887969i	$-0.347884\pi$
$821$	619988.			0.919807			0.459903	+	0.887969i	$0.347884\pi$
$822$	97830.8	−	97830.8i	0.144788	−	0.144788i
$823$	643329.			0.949802			0.474901	−	0.880039i	$-0.342484\pi$
$823$	643329.			0.949802			0.474901	+	0.880039i	$0.342484\pi$
$824$	−313865.			−0.462263
$825$		−	222750.i		−	0.327273i
$826$	182184.			0.267025
$827$	549710.	−	549710.i	0.803753	−	0.803753i	−0.179927	−	0.983680i	$-0.557586\pi$
$827$	549710.	−	549710.i	0.803753	−	0.803753i	0.983680	+	0.179927i	$0.0575862\pi$
$828$	190.725	+	190.725i	0.000278193	+	0.000278193i
$829$	75182.7	+	75182.7i	0.109398	+	0.109398i	0.759687	−	0.650289i	$-0.225352\pi$
$829$	75182.7	+	75182.7i	0.109398	+	0.109398i	−0.650289	+	0.759687i	$0.725352\pi$
$830$	1.13727e6			1.65085
$831$	426057.	−	426057.i	0.616972	−	0.616972i
$832$	111199.	+	111199.i	0.160641	+	0.160641i
$833$	−13091.9	+	13091.9i	−0.0188674	+	0.0188674i
$834$	−646742.	−	646742.i	−0.929820	−	0.929820i
$835$			263061.i			0.377297i
$836$	327.782	−	327.782i	0.000469000	−	0.000469000i
$837$	533970.	−	533970.i	0.762195	−	0.762195i
$838$	274033.	+	274033.i	0.390225	+	0.390225i
$839$		−	898102.i		−	1.27586i	−0.770096	−	0.637928i	$-0.779792\pi$
$839$		−	898102.i		−	1.27586i	0.770096	−	0.637928i	$-0.220208\pi$
$840$	352523.			0.499607
$841$			1.87788e6i			2.65508i
$842$		−	171441.i		−	0.241819i
$843$	345383.	+	345383.i	0.486010	+	0.486010i
$844$			121459.i			0.170508i
$845$	1.85276e6	+	1.85276e6i	2.59481	+	2.59481i
$846$	10737.6	+	10737.6i	0.0150026	+	0.0150026i
$847$	−547999.			−0.763859
$848$	30611.2			0.0425686
$849$	846789.	−	846789.i	1.17479	−	1.17479i
$850$		−	56390.1i		−	0.0780486i
$851$	−2206.92	+	475.185i	−0.00304739	+	0.000656151i
$852$	249556.			0.343786
$853$	123126.	+	123126.i	0.169220	+	0.169220i	0.786637	−	0.617416i	$-0.211821\pi$
$853$	123126.	+	123126.i	0.169220	+	0.169220i	−0.617416	+	0.786637i	$0.711821\pi$
$854$		−	147180.i		−	0.201806i
$855$			2052.15i			0.00280722i
$856$	355268.	−	355268.i	0.484851	−	0.484851i
$857$	−100688.	+	100688.i	−0.137093	+	0.137093i	−0.772323	−	0.635230i	$-0.780905\pi$
$857$	−100688.	+	100688.i	−0.137093	+	0.137093i	0.635230	+	0.772323i	$0.280905\pi$
$858$	−201218.			−0.273334
$859$	−533548.	+	533548.i	−0.723082	+	0.723082i	−0.969232	−	0.246150i	$-0.920834\pi$
$859$	−533548.	+	533548.i	−0.723082	+	0.723082i	0.246150	+	0.969232i	$0.420834\pi$
$860$	−558316.			−0.754889
$861$	−906968.			−1.22345
$862$			908796.i			1.22307i
$863$	1.40423e6			1.88546			0.942730	−	0.333556i	$-0.108248\pi$
$863$	1.40423e6			1.88546			0.942730	+	0.333556i	$0.108248\pi$
$864$	−78067.5	+	78067.5i	−0.104579	+	0.104579i
$865$	−1.11040e6	−	1.11040e6i	−1.48405	−	1.48405i
$866$	−567893.	−	567893.i	−0.757236	−	0.757236i
$867$	836898.			1.11336
$868$	271978.	−	271978.i	0.360989	−	0.360989i
$869$	−134004.	−	134004.i	−0.177451	−	0.177451i
$870$	1.29015e6	−	1.29015e6i	1.70452	−	1.70452i
$871$	−1.24925e6	−	1.24925e6i	−1.64669	−	1.64669i
$872$			16966.7i			0.0223134i
$873$	−32022.3	+	32022.3i	−0.0420170	+	0.0420170i
$874$	8.31010	−	8.31010i	1.08789e−5	−	1.08789e-5i
$875$	−368273.	−	368273.i	−0.481010	−	0.481010i
$876$		−	200365.i		−	0.261105i
$877$	1.46442e6			1.90400			0.952001	−	0.306096i	$-0.0990229\pi$
$877$	1.46442e6			1.90400			0.952001	+	0.306096i	$0.0990229\pi$
$878$			867149.i			1.12488i
$879$			1.44014e6i			1.86392i
$880$	41454.4	+	41454.4i	0.0535310	+	0.0535310i
$881$		−	212596.i		−	0.273906i	−0.990578	−	0.136953i	$-0.956269\pi$
$881$		−	212596.i		−	0.273906i	0.990578	−	0.136953i	$-0.0437310\pi$
$882$	36520.6	+	36520.6i	0.0469463	+	0.0469463i
$883$	247045.	+	247045.i	0.316851	+	0.316851i	0.847556	−	0.530705i	$-0.178073\pi$
$883$	247045.	+	247045.i	0.316851	+	0.316851i	−0.530705	+	0.847556i	$0.678073\pi$
$884$	−50939.3			−0.0651851
$885$	−665496.			−0.849687
$886$	−301805.	+	301805.i	−0.384467	+	0.384467i
$887$		−	1.12058e6i		−	1.42429i	−0.702034	−	0.712143i	$-0.747725\pi$
$887$		−	1.12058e6i		−	1.42429i	0.702034	−	0.712143i	$-0.252275\pi$
$888$	65673.7	+	305011.i	0.0832848	+	0.386802i
$889$	361886.			0.457897
$890$	−1.04957e6	−	1.04957e6i	−1.32504	−	1.32504i
$891$		−	179350.i		−	0.225916i
$892$		−	358813.i		−	0.450961i
$893$	467.850	−	467.850i	0.000586684	−	0.000586684i
$894$	−494778.	+	494778.i	−0.619064	+	0.619064i
$895$	−1.01441e6			−1.26639
$896$	−39763.6	+	39763.6i	−0.0495302	+	0.0495302i
$897$	−5101.39			−0.00634021
$898$	−576886.			−0.715381
$899$		−	1.99075e6i		−	2.46318i
$900$	−157304.			−0.194203
$901$	−7011.35	+	7011.35i	−0.00863678	+	0.00863678i
$902$	−106654.	−	106654.i	−0.131088	−	0.131088i
$903$	484541.	+	484541.i	0.594230	+	0.594230i
$904$	329353.			0.403019
$905$	−809475.	+	809475.i	−0.988340	+	0.988340i
$906$	478428.	+	478428.i	0.582855	+	0.582855i
$907$	211571.	−	211571.i	0.257182	−	0.257182i	−0.566725	−	0.823907i	$-0.691790\pi$
$907$	211571.	−	211571.i	0.257182	−	0.257182i	0.823907	+	0.566725i	$0.191790\pi$
$908$	215988.	+	215988.i	0.261974	+	0.261974i
$909$		−	142020.i		−	0.171878i
$910$	−950193.	+	950193.i	−1.14744	+	1.14744i
$911$	−694787.	+	694787.i	−0.837173	+	0.837173i	−0.988486	−	0.151313i	$-0.951650\pi$
$911$	−694787.	+	694787.i	−0.837173	+	0.837173i	0.151313	+	0.988486i	$0.451650\pi$
$912$	−1148.51	−	1148.51i	−0.00138085	−	0.00138085i
$913$		−	232129.i		−	0.278476i
$914$	−215159.			−0.257553
$915$			537631.i			0.642158i
$916$			354492.i			0.422489i
$917$	−551114.	−	551114.i	−0.655395	−	0.655395i
$918$		−	35762.0i		−	0.0424361i
$919$	−737706.	−	737706.i	−0.873479	−	0.873479i	0.119371	−	0.992850i	$-0.461912\pi$
$919$	−737706.	−	737706.i	−0.873479	−	0.873479i	−0.992850	+	0.119371i	$0.961912\pi$
$920$	1050.97	+	1050.97i	0.00124170	+	0.00124170i
$921$	−262860.			−0.309889
$922$	−273443.			−0.321666
$923$	−672655.	+	672655.i	−0.789567	+	0.789567i
$924$		−	71953.4i		−	0.0842767i
$925$	714142.	−	1.10606e6i	0.834644	−	1.29269i
$926$	−153494.			−0.179007
$927$	−200540.	−	200540.i	−0.233368	−	0.233368i
$928$			291051.i			0.337966i
$929$		−	74954.4i		−	0.0868492i	−0.999057	−	0.0434246i	$-0.986173\pi$
$929$		−	74954.4i		−	0.0868492i	0.999057	−	0.0434246i	$-0.0138268\pi$
$930$	−993499.	+	993499.i	−1.14869	+	1.14869i
$931$	1591.25	−	1591.25i	0.00183586	−	0.00183586i
$932$	573588.			0.660340
$933$	−87794.4	+	87794.4i	−0.100856	+	0.100856i
$934$	481724.			0.552210
$935$	−18989.9			−0.0217219
$936$			142099.i			0.162195i
$937$	−1.30338e6			−1.48454			−0.742272	−	0.670099i	$-0.766252\pi$
$937$	−1.30338e6			−1.48454			−0.742272	+	0.670099i	$0.766252\pi$
$938$	446717.	−	446717.i	0.507722	−	0.507722i
$939$	335323.	+	335323.i	0.380305	+	0.380305i
$940$	59168.8	+	59168.8i	0.0669633	+	0.0669633i
$941$	−1.05674e6			−1.19341			−0.596704	−	0.802461i	$-0.703523\pi$
$941$	−1.05674e6			−1.19341			−0.596704	+	0.802461i	$0.703523\pi$
$942$	−150804.	+	150804.i	−0.169946	+	0.169946i
$943$	−2703.94	−	2703.94i	−0.00304070	−	0.00304070i
$944$	75066.3	−	75066.3i	0.0842366	−	0.0842366i
$945$	−667083.	−	667083.i	−0.746992	−	0.746992i
$946$			113958.i			0.127339i
$947$	845570.	−	845570.i	0.942866	−	0.942866i	−0.0555880	−	0.998454i	$-0.517703\pi$
$947$	845570.	−	845570.i	0.942866	−	0.942866i	0.998454	+	0.0555880i	$0.0177034\pi$
$948$	−469534.	+	469534.i	−0.522456	+	0.522456i
$949$	540067.	+	540067.i	0.599674	+	0.599674i
$950$			6853.93i			0.00759438i
$951$	156463.			0.173001
$952$		−	18215.3i		−	0.0200985i
$953$			421080.i			0.463638i	0.972759	+	0.231819i	$0.0744676\pi$
$953$			421080.i			0.463638i	−0.972759	+	0.231819i	$0.925532\pi$
$954$	19558.6	+	19558.6i	0.0214903	+	0.0214903i
$955$			2.12888e6i			2.33424i
$956$	273260.	+	273260.i	0.298992	+	0.298992i
$957$	−263332.	−	263332.i	−0.287528	−	0.287528i
$958$	748730.			0.815820
$959$	−188588.			−0.205058
$960$	145251.	−	145251.i	0.157608	−	0.157608i
$961$			609485.i			0.659958i
$962$	−999147.	−	645111.i	−1.07964	−	0.697083i
$963$	453988.			0.489544
$964$	65777.6	+	65777.6i	0.0707822	+	0.0707822i
$965$			2.29514e6i			2.46465i
$966$		−	1824.20i		−	0.00195487i
$967$	−88794.4	+	88794.4i	−0.0949582	+	0.0949582i	−0.752990	−	0.658032i	$-0.771389\pi$
$967$	−88794.4	+	88794.4i	−0.0949582	+	0.0949582i	0.658032	+	0.752990i	$0.271389\pi$
$968$	−225795.	+	225795.i	−0.240970	+	0.240970i
$969$	526.121			0.000560323
$970$	−176457.	+	176457.i	−0.187540	+	0.187540i
$971$	826023.			0.876100			0.438050	−	0.898951i	$-0.355669\pi$
$971$	826023.			0.876100			0.438050	+	0.898951i	$0.355669\pi$
$972$	−233205.			−0.246834
$973$			1.24672e6i			1.31687i
$974$	−703853.			−0.741932
$975$	2.10374e6	−	2.10374e6i	2.21301	−	2.21301i
$976$	−60643.4	−	60643.4i	−0.0636625	−	0.0636625i
$977$	1.19428e6	+	1.19428e6i	1.25117	+	1.25117i	0.955197	+	0.295971i	$0.0956433\pi$
$977$	1.19428e6	+	1.19428e6i	1.25117	+	1.25117i	0.295971	+	0.955197i	$0.404357\pi$
$978$	18147.7			0.0189733
$979$	−214227.	+	214227.i	−0.223516	+	0.223516i
$980$	201244.	+	201244.i	0.209542	+	0.209542i
$981$	−10840.7	+	10840.7i	−0.0112647	+	0.0112647i
$982$	−86867.4	−	86867.4i	−0.0900811	−	0.0900811i
$983$			1.02988e6i			1.06581i	0.846175	+	0.532906i	$0.178900\pi$
$983$			1.02988e6i			1.06581i	−0.846175	+	0.532906i	$0.821100\pi$
$984$	−373702.	+	373702.i	−0.385954	+	0.385954i
$985$	1.94988e6	−	1.94988e6i	2.00972	−	2.00972i
$986$	−66663.8	−	66663.8i	−0.0685703	−	0.0685703i
$987$		−	102701.i		−	0.105424i
$988$	6191.41			0.00634272
$989$			2889.12i			0.00295374i
$990$			52973.5i			0.0540491i
$991$	138293.	+	138293.i	0.140816	+	0.140816i	0.774001	−	0.633185i	$-0.218253\pi$
$991$	138293.	+	138293.i	0.140816	+	0.140816i	−0.633185	+	0.774001i	$0.718253\pi$
$992$		−	224128.i		−	0.227758i
$993$	1.53903e6	+	1.53903e6i	1.56081	+	1.56081i
$994$	−240534.	−	240534.i	−0.243446	−	0.243446i
$995$	−1.95952e6			−1.97926
$996$	−813353.			−0.819899
$997$	−315913.	+	315913.i	−0.317817	+	0.317817i	−0.847928	−	0.530111i	$-0.822150\pi$
$997$	−315913.	+	315913.i	−0.317817	+	0.317817i	0.530111	+	0.847928i	$0.322150\pi$
$998$		−	1.20264e6i		−	1.20747i
$999$	452901.	−	701451.i	0.453808	−	0.702856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.d.b.31.2	✓	14
37.6	odd	4	inner	74.5.d.b.43.6	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.b.31.2	✓	14	1.1	even	1	trivial
74.5.d.b.43.6	yes	14	37.6	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} -10.0720i q^{3} +8.00000i q^{4} +(-28.1665 + 28.1665i) q^{5} +(20.1441 - 20.1441i) q^{6} -38.8317 q^{7} +(-16.0000 + 16.0000i) q^{8} -20.4460 q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} -10.0720i q^{3} +8.00000i q^{4} +(-28.1665 + 28.1665i) q^{5} +(20.1441 - 20.1441i) q^{6} -38.8317 q^{7} +(-16.0000 + 16.0000i) q^{8} -20.4460 q^{9} -112.666 q^{10} +22.9963i q^{11} +80.5763 q^{12} +(-217.186 + 217.186i) q^{13} +(-77.6634 - 77.6634i) q^{14} +(283.694 + 283.694i) q^{15} -64.0000 q^{16} +(14.6589 - 14.6589i) q^{17} +(-40.8920 - 40.8920i) q^{18} +(-1.78171 + 1.78171i) q^{19} +(-225.332 - 225.332i) q^{20} +391.114i q^{21} +(-45.9926 + 45.9926i) q^{22} +(-1.16603 + 1.16603i) q^{23} +(161.153 + 161.153i) q^{24} -961.706i q^{25} -868.745 q^{26} -609.902i q^{27} -310.653i q^{28} +(-1136.92 - 1136.92i) q^{29} +1134.78i q^{30} +(875.501 + 875.501i) q^{31} +(-128.000 - 128.000i) q^{32} +231.620 q^{33} +58.6355 q^{34} +(1093.75 - 1093.75i) q^{35} -163.568i q^{36} +(1150.10 + 742.579i) q^{37} -7.12685 q^{38} +(2187.51 + 2187.51i) q^{39} -901.329i q^{40} +2318.93i q^{41} +(-782.229 + 782.229i) q^{42} +(1238.87 - 1238.87i) q^{43} -183.970 q^{44} +(575.892 - 575.892i) q^{45} -4.66411 q^{46} -262.585 q^{47} +644.611i q^{48} -893.100 q^{49} +(1923.41 - 1923.41i) q^{50} +(-147.645 - 147.645i) q^{51} +(-1737.49 - 1737.49i) q^{52} -478.300 q^{53} +(1219.80 - 1219.80i) q^{54} +(-647.725 - 647.725i) q^{55} +(621.307 - 621.307i) q^{56} +(17.9455 + 17.9455i) q^{57} -4547.67i q^{58} +(-1172.91 + 1172.91i) q^{59} +(-2269.55 + 2269.55i) q^{60} +(947.553 + 947.553i) q^{61} +3502.01i q^{62} +793.952 q^{63} -512.000i q^{64} -12234.8i q^{65} +(463.239 + 463.239i) q^{66} +5751.96i q^{67} +(117.271 + 117.271i) q^{68} +(11.7443 + 11.7443i) q^{69} +4375.01 q^{70} +3097.13 q^{71} +(327.136 - 327.136i) q^{72} -2486.65i q^{73} +(815.050 + 3785.36i) q^{74} -9686.34 q^{75} +(-14.2537 - 14.2537i) q^{76} -892.985i q^{77} +8750.03i q^{78} +(-5827.19 + 5827.19i) q^{79} +(1802.66 - 1802.66i) q^{80} -7799.09 q^{81} +(-4637.87 + 4637.87i) q^{82} -10094.2 q^{83} -3128.91 q^{84} +825.779i q^{85} +4955.49 q^{86} +(-11451.1 + 11451.1i) q^{87} +(-367.941 - 367.941i) q^{88} +(9315.73 + 9315.73i) q^{89} +2303.57 q^{90} +(8433.71 - 8433.71i) q^{91} +(-9.32822 - 9.32822i) q^{92} +(8818.09 - 8818.09i) q^{93} +(-525.169 - 525.169i) q^{94} -100.369i q^{95} +(-1289.22 + 1289.22i) q^{96} +(1566.19 - 1566.19i) q^{97} +(-1786.20 - 1786.20i) q^{98} -470.182i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9}+O(q^{10}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9	\( 14 q + 28 q^{2} + 36 q^{5} + 40 q^{6} - 48 q^{7} - 224 q^{8} - 346 q^{9} + 144 q^{10} + 160 q^{12} - 104 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} + 516 q^{17} - 692 q^{18} - 328 q^{19} + 288 q^{20} - 320 q^{22} + 154 q^{23} + 320 q^{24} - 416 q^{26} + 1686 q^{29} + 3834 q^{31} - 1792 q^{32} + 2104 q^{33} + 2064 q^{34} - 1502 q^{35} + 2640 q^{37} - 1312 q^{38} - 4526 q^{39} - 5984 q^{42} + 3616 q^{43} - 1280 q^{44} - 2238 q^{45} + 616 q^{46} - 6892 q^{47} + 12854 q^{49} + 7516 q^{50} - 6742 q^{51} - 832 q^{52} + 12572 q^{53} - 1072 q^{54} + 5510 q^{55} + 768 q^{56} - 6302 q^{57} - 8422 q^{59} + 3024 q^{60} - 6386 q^{61} + 22244 q^{63} + 4208 q^{66} + 4128 q^{68} + 1728 q^{69} - 6008 q^{70} + 8680 q^{71} + 5536 q^{72} + 1316 q^{74} - 37980 q^{75} - 2624 q^{76} - 28520 q^{79} - 2304 q^{80} - 33962 q^{81} + 9136 q^{82} - 22688 q^{83} - 23936 q^{84} + 14464 q^{86} + 1828 q^{87} - 2560 q^{88} + 18344 q^{89} - 8952 q^{90} - 4918 q^{91} + 1232 q^{92} + 24 q^{93} - 13784 q^{94} - 2560 q^{96} + 23246 q^{97} + 25708 q^{98}+O(q^{100}) \) 14 * q + 28 * q^2 + 36 * q^5 + 40 * q^6 - 48 * q^7 - 224 * q^8 - 346 * q^9 + 144 * q^10 + 160 * q^12 - 104 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 + 516 * q^17 - 692 * q^18 - 328 * q^19 + 288 * q^20 - 320 * q^22 + 154 * q^23 + 320 * q^24 - 416 * q^26 + 1686 * q^29 + 3834 * q^31 - 1792 * q^32 + 2104 * q^33 + 2064 * q^34 - 1502 * q^35 + 2640 * q^37 - 1312 * q^38 - 4526 * q^39 - 5984 * q^42 + 3616 * q^43 - 1280 * q^44 - 2238 * q^45 + 616 * q^46 - 6892 * q^47 + 12854 * q^49 + 7516 * q^50 - 6742 * q^51 - 832 * q^52 + 12572 * q^53 - 1072 * q^54 + 5510 * q^55 + 768 * q^56 - 6302 * q^57 - 8422 * q^59 + 3024 * q^60 - 6386 * q^61 + 22244 * q^63 + 4208 * q^66 + 4128 * q^68 + 1728 * q^69 - 6008 * q^70 + 8680 * q^71 + 5536 * q^72 + 1316 * q^74 - 37980 * q^75 - 2624 * q^76 - 28520 * q^79 - 2304 * q^80 - 33962 * q^81 + 9136 * q^82 - 22688 * q^83 - 23936 * q^84 + 14464 * q^86 + 1828 * q^87 - 2560 * q^88 + 18344 * q^89 - 8952 * q^90 - 4918 * q^91 + 1232 * q^92 + 24 * q^93 - 13784 * q^94 - 2560 * q^96 + 23246 * q^97 + 25708 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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